Conventional communications systems include a transmitter for generating waveforms, a transmission medium for transporting the generated waveforms, and a receiver for receiving and processing transmitted waveforms. On the transmission side, information may be digitally encoded into a data stream using a number of algorithms. The encoded data stream is modulated on a carrier by one or more modulation techniques, including for example one of the several forms of phase-shift-keying (PSK). In the receiver, the original data stream is recovered by reversing the processing steps performed in the transmitter, and also by compensating for noise and other errors added to the signal during transmission and reception.
A demodulator is typically provided on the receiving end for performing a number of tasks. In a PSK modulated system, PSK demodulators translate the received signal into in-phase (I) and quadrature (Q) components, and then recover the transmitted message from I and Q. PSK demodulators also perform phase synchronization, which involves making an estimate of the absolute carrier phase.
In "closed loop" phase synchronization, a phase error detector detects the presence of a carrier phase error, and an estimate of the carrier phase error is calculated and fed back to the phase synchronizer. In general, an estimate of the carrier phase error associated with I and Q may be determined by calculating an arctangent. The arctangent, however, is a complicated calculation that would be difficult to perform for every received symbol. Accordingly, the appropriate arctangent calculations are typically stored in a look-up table in the demodulator's memory (ROM or RAM). Assuming that the value range of the look-up table spans from negative 128 to positive 127 for both I and Q, and assuming that the phase-error-estimate is represented by an 8-bit word, the required look-up table would occupy 256.times.256.times.8 memory spaces, or approximately 64 Kbytes of memory.
Accordingly, it would be beneficial to provide a method and apparatus for estimating phase errors in a phase-modulated signal, whereby the amount of ROM or RAM needed to store a phase-error-estimate look-up table is reduced.